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A classification of groups with a centralizer condition II

Published online by Cambridge University Press:  17 April 2009

Zvi Arad  and
Marcel Herzog
Zvi Arad
Affiliation:
Department of Mathematics, Bar Ilan University, Ramat-Gan, Israel;
Marcel Herzog
Affiliation:
Department of Mathematics, Institute of Advanced Studies, AustraIian National University, Canberra, ACT.
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Abstract

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Let G be a finite group. A nontrivial proper subgroup M of G is called a CC-subgpoup if M contains the centralizer in G of each of its nonidentity elements. In this paper groups containing a CC-subgroup of order divisible by 3 are completely determined.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 1 , February 1977 , pp. 55 - 60
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Arad, Zvi, “A classification of groups with a centralizer condition”, Bull. Austral. Math. Soc. 15 (1976), 81–85.CrossRefGoogle Scholar
[2]Arad, Zvi, “A classification of 3CC-groups and applications to Glauberman-Goldschmidt theorem”, submitted.Google Scholar
[3]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar
[4]Higman, Graham, Odd characterisations of finite simple groups (Lecture Notes, University of Michigan, 1968).Google Scholar
[5]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[6]Stewart, W.B., “Groups having strongly self-centralizing 3-centralizers”, Proc. London Math. Soc. (3) 26 (1973), 653–680.CrossRefGoogle Scholar
[7]Stewart, W.B., “Finite simple groups having an element of order three whose centralizer is of order fifteen”, Quart. J. Math. Oxford (2) 25 (1974), 9–17.CrossRefGoogle Scholar
[8]Suzuki, Michio, “Two characteristic properties of (ZT)-groups”, Osaka Math. J. 15 (1963), 143–150.Google Scholar
[9]Walter, John H., “The characterization of finite groups with abelian Sylow 2-subgroups”, Ann. of Math. (2) 89 (1969), 405–514.CrossRefGoogle Scholar